A Discriminant Function for Earnings-Price Ratios of Large Industrial Corporations

T HE intent of this study is to ascertain that linear combination of financial characteristics which best discriminates large industrial corporations with low ratios of earnings per share to common stock price from those with high ratios.' The linear transformation of several variables into a single variate (z) permits the categorization of firms on the basis of whether the z values are greater or less than a predetermined mean value. The proposition which underlies the division of firms into high and low ratio groups is that, if allowance is made for the historical nature of earnings and for market imperfections, the earnings-to-stock-price ratio reflects the composite market valuation of such factors as financial risk and dividend policy.2 With this in mind, it is interesting to inquire whether certain basic measures can be used to differentiate successfully between the two classes. Discriminating variables, that is, financial characteristics chosen to reflect individual elements of risk and other factors which affect e/p ratios, include the ratio of dividends to earnings, the ratio of current assets to current liabilities, the rate of return on additional investment, the relative change in sales, and the comparative stability of the common stock price. The construction of the problem is designed to parallel the thinking of investors and/or financial executives. Despite the apparent continuity of risk gradations, firms tend to be grouped on the basis of low, medium, and high risk; e/p ratios (or their reciprocals) are often used as the initial stratification variable; and attention is customarily directed to the extreme classes. The evaluation of common stock and other corporate securities tends in ddition -to be carried out in terms of certain conventional ratios. Discriminant analysis, as employed here, is not intended as a substitute for multiple regression analysis. Given little knowledge as to the appropriate form and complexity of the general regression function, this approach nonetheless serves as a useful device for observing directly those characteristics which distinguish lowand high-risk categories. The relevant information obtained is large relative to the sample size. The derived relationships may in turn facilitate the formulation of multiple regression functions. The potential utility of the analysis which follows is at least threefold. First, procedures for the selection of underand overvalued stocks may be improved by the introduction of discriminant analysis. If the discriminating index suggests that a firm clearly belongs to one group while its e/p ratio indicates otherwise, some reason exists for believing the company's stock to be underor overpriced. Second, partial conclusions may be drawn as to the influence of changing stock market levels upon the importance of different factors which condition e/p ratios. Distributions of e/p ratios, exhibited in Table i for samples of large industrial firms, reflect (for example) a greater central tendency for the I952-55 period than for I948-5I. If the discriminating function based upon the I952-55 data fails to predict well for the earlier period, there is some presumption that weights of the individual variables have shifted. The index characteristic of discriminant analysis affords certain advantages in this respect. The discriminant function is applicable whatever the level of stock prices, provided the * The helpful assistance of W. W. Cooper and Carl Hensley, Carnegie Institute of Technology, and Charles Christenson, Harvard University, is acknowledged. The computations were performed in the computer center at Carnegie Institute of Technology. I The method employed is described in G. Tintner, Econometrics (New York, 1952), 96-I02. See also M. G. Kendall, The Advanced Theory of Statistics (London, I946), Vol. ii, 34I-48. By "best discriminates" is meant that the chance of erroneous classification is approximately minimal. 2Earnings-to-stock-price ratios are hereafter referred to as e/p ratios.